The effect of magnitude uncertainty on the Gutenberg–Richter b-value estimation and the magnitude–frequency distribution: ‘what hump?’

Abstract

The uncertainties on magnitudes of the earthquakes have a negligible effect on the estimation of the Gutenberg–Richter b-value if these uncertainties have a homogeneous distribution, that is, the magnitude error is the same for all the earthquakes. Here, we show that a non-uniform error distribution can have a significant impact on the b-value estimation, and it generates a hump in the magnitude–frequency distribution. Through a simulation approach, we show when the bias in the estimation is large, when it can be neglected, and how it is possible to avoid it.